ECI, which owns a controlling stake in the Dublin-based business, is about to hire PricewaterhouseCoopers to advise on an auction according to Sky News, which did not say where the information came from.
The firm bought CarTrawler for about £80m in 2011, and bolted on the online arm of Holiday Assets earlier this summer.
Those assets included Holiday Autos, which ECI owned previously for several years before selling the business in 2003.
The firm invested in the off-licence and convenience store group in 2006. The company operates over 600 franchisee-owned stores in the North West of England under the Bargain Booze brand.
Conviviality Retail was admitted with a market capitalisation of £66.7m in the largest IPO exit by a corporate on AIM so far this year. The fundraising was twice over-subscribed with over 30 participating institutions.
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